7. Find (f•g)(x) for the pair of functions.
f(x)=x+1
g(x) = 4x - 11
(f•g)(x) =

Answer: 2 radians

Step-by-step explanation: You welcome

The rate of the slower jet is 672 miles per hour.

The rate of the slower jet is 752 miles per hour.

Two jets leave an air base at the same time and travel in opposite directions.

One jet travels 80 mi/h faster than the other.

let

x = rate of the slower jet

faster jet = 80 + x

Therefore,

rate = distance / time

The two jets are 11392 miles apart.

(80 + x)8 + 8x = 11392

640 + 8x + 8x = 11392

640 + 16x = 11392

16x = 11392 - 640

16x = 10752

divide both sides by 16

x = 10752 / 16

x = 672 miles per hour

rate of the faster jet = 80 + 672 = 752 miles per hour

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Answer:

m∠RQS = 109°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore:

⇒ m∠RQS + m∠SQT = 180°

⇒ (15x + 4) + (10x + 1) = 180

⇒ 15x + 4 + 10x + 1 = 180

⇒ 15x + 10x + 4 + 1 = 180

⇒ 25x + 5 = 180

⇒ 25x + 5 - 5 = 180 - 5

⇒ 25x = 175

⇒ 25x ÷ 25 = 175 ÷ 25

⇒ x = 7

Now that we have found the value of x, substitute this into the expression for m∠RQS:

⇒ m∠RQS = 15(7) + 4

                  = 105 + 4

                  = 109°

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The equivalent expression for the given expression is 28p + 14q + 21r.

An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.

An equivalent expression is simplified to the original expression by using the distributive property.

The distributive property is

a(b + c) = ab + ac

The given expression is 7(4p + 2q + 3r)

Applying the distributive property,

7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)

⇒ 28p + 14q + 21r

Thus, the equivalent expression for the given expression is 28p + 14q + 21r.

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7(4p+2q+3r)=7(4p+2q+3r)

Apply distributive law

So

This is the required expression

Answer:

a. 33

Step-by-step explanation:

a straight line is 180° so

3x = 180 - 81

3x = 99

to find x divide by 3

x = 99/3

x = 33

Answer:

2 dogs

Step-by-step explanation:

Answer: 0

Step-by-step explanation: I am going by the words , there WERE 3 ponies. So Sarah couldn’t take any rides.

Step-by-step explanation:

Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))

Answer:

[tex]\bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]

Step-by-step explanation:

There was no figure but the question is clear

Volume of a cylinder is given by the formula [tex]\bold{\pi r^2h}\\[/tex]

where r is radius of base of cylinder, h is the height

Volume of a cone is given by [tex]\bold{\frac{1}{3} \pi r^2 h}[/tex]

where r is the radius of base of cone, h is the height

The radius of the cylinder = [tex]\frac{1}{2}[/tex](diameter) = [tex]\frac{1}{2}[/tex](12) = 6cm

Height of cylinder = 15cm

Volume of cylinder [tex]V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}[/tex]

Radius of cone = [tex]\frac{1}{2}[/tex] (radius of cylinder) = [tex]\frac{1}{2}[/tex](6) = 3 cm

Height of cone same as height of cylinder = 15cm

Volume of cone, [tex]V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\[/tex]

Difference is the volume of the remaining solid

[tex]V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]

One second later, the distance between the two stones will change in a speed of 6.86 m/s

Distance can be defined as the length of change of position. When an object change from one position to another, the length between the points or position is known as distance.

If a dropped stone has a distance d = 4.9t²

Let us assumed that the time taken = 3 seconds

The distance d = 4.9 × 3² = 44.1 m

If another stone is dropped one second later, then the time t = 4 s

The distance = 4.9 × 4² = 78.4 m

One second later, the time = 5 seconds

The speed of change in distance = ( 78.4 - 44.1 )/ 5

The speed of change in distance = 34.3 / 5

The speed of change in distance = 6.86 m/s

Therefore, one second later, the distance between the two stones will change in 6.86 m/s

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Answer:

[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}=\frac{4}{9}[/tex]

Step-by-step explanation:

[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}[/tex]

Pull out  n³

[tex]=\lim_{n\rightarrow +\infty } \frac{n^{3}\times \left( 4-\frac{5}{n^3} \right) }{n^{3}\times \left( 9+\frac{7}{n^3} \right) }[/tex]

Simplify by n³

[tex]=\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }[/tex]

Remark : [tex]\lim_{n\rightarrow +\infty } \frac{5}{n^3} \right) } = 0 \ \. \text{and} \ \ \lim_{n\rightarrow +\infty } \frac{7}{n^3} \right) } = 0[/tex]

Then

[tex]\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }=\frac{4-0}{9+0}[/tex]

[tex]=\frac{4}{9}[/tex]

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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The factor of given expression is 6(5-v-3w) and 2(15-3v-9w). correct option is c and d.

Given that factor 30-6v-18w.

Equivalent expressions are expressions that work the same way, even if they look different. If two algebraic expressions are equivalent, the two expressions have the same value if we enter the same values ​​for the variables.

For option A

Factor the expression:

2(15-2v)≠6(5-v-3w)

get the result: False

Answer: False

For option B

Factor the expression:

3(10-3v+6w)≠6(5-v-3w)

get the result: False

For option C

Factor the expression:

6(5-v-3w)=6(5-v-3w)

get the result: True

For option D

Factor the expression:

6(5-v-3w)=2(15-3v-9w)

get the result: True

Hence, the equivalent expression of the factor 30-6v-18w is 6(5-v-3w) and 2(15-3v-9w).

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The probability that this adult used non-prescription antidepressants is 0.78.

Based on the information given, the following can be deduced:

Let A = event where adults visit therapist.

Let B = event where adults used non prescription antidepressants.

P(A) = 0.27

P(B) = 0.46

P(A n B) = 0.21

The probability that a randomly selected adult who visited the therapist used non-prescription antidepressants will be:

= 0.21/0.27

= 0.78

The probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants will be:

= 0.21/0.46

= 0.46

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Answer:

0

Step-by-step explanation:

hi

hi

haha

and

and

are doing

dog food

0 answer

(scroll to bottom for answer)The equation you want to be using is A(n)+1=(A(n))r because this is a exponential sequence

r represents the ratio, which you said was 25, so basically you said

A(n)

____     = 25

A(n)-1

rthe sum of the first 2 terms are 16, the first two terms being A1 and A2, they need to follow the equation:

A2

__  = 25

A1

lets give them variables to make this a bit easier-

A1 will be x and A2 will be y

x+y=16(1st equation)

y/x=25, 25x=y(2nd equation)

(if you multiply y/x=25 by x you will get that 25x=y, which is where that other equation came from)

going back to x+y=16

subtract y from both sides

x=16-y

use substitution and solve for the second equation

25(16-y)=y

distribute

400-25y=y

add 25y to both sides to get rid of the -25y on the left side while keeping the equation equal

400=26y

divide both sides by 26 and you get 400/26 which simplifies to 200/13

after all that you need to multiply 200/13 by 25, 3 separate times

200                              1875000

___ x 25 x 25 x 25= _________

13                                      13

pull it into a calculator and you get something like

142846.153846

Answer:

2

Step-by-step explanation:

a23

2 is column and 3 is row

2/3 is 400% of 1/6

0.2 is 12.5% of 1 3/5

From the question, we are to determine what percent of 1/6 is 2/3

Let the value be x

Thus,

We can write that

2/3 is x% of 1/6

This means

2/3 = x/100 × 1/6

Now, solve for x

2/3 = x/100 × 1/6

2/3 = x/600

x = (2×600)/3

x = 400

Hence, 2/3 is 400% of 1/6

We are to determine what percent of 1 3/5 is 0.2

Let the value be y

That is,

0.2 is y% of 1 3/5

This can be written as

0.2 = y% × 1.6

0.2 = y/100 × 1.6

Now, solve for y

0.2 = y/100 × 1.6

0.2 = 1.6y/100

1.6y = 0.2 × 100

1.6y = 20

y = 20/1.6
y = 12.5

Hence, 0.2 is 12.5% of 1 3/5

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The average number of pages she reads per hour is 19 pages per hour

The given parameters are:

Number of pages = 76 pages

Number of hours = 4 hours

The average number of pages she reads per hour is calculated using the following formula

Average = Number of pages/Number of hours

Substitute the known values in the above equation

Average = 76 pages/4 hours

Evaluate the quotient

Average = 19 pages per hours

Hence, the average number of pages she reads per hour is 19 pages per hours

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The measure of angle a is 70 degrees

The angle in a semicircle is a right angle.

This means that:

a + d = 90

Where O is the center of the circle

From the figure, we have:

Angle d and the angle with a measure of 20 degrees are corresponding angles

This means that

d = 20

Substitute d = 20 in a + d = 90

a + 20 = 90

Subtract 20 from both sides of the equation

a = 70

Hence, the measure of angle a is 70 degrees

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Answer:

No, it is not a one-to-one function.

Step-by-step explanation:

A one-to-one function means a value of y will only exist one value of x. This means that a value of y will only have one value of x.

An example of one-to-one function is an odd-degree polynomial such as linear function.

An example of non one-to-one function is a parabola since a value of y exists two values of x.

From the question, this function represents a graph of half circle with radius equal to [tex]\displaystyle{\sqrt{5}}[/tex]. (The graph has been attached below for visual reference.)

There's also a way to determine whether if a function is one-to-one or not. This can be done by drawing a horizontal line.

From the graph and a horizontal line, both have two common points. Therefore, the function is not a one-to-one function.

* The red graph represents the given function while blue graph is a horizontal line determining a one-to-one function or not *

The least miles per gallon this trip is 25 miles per gallon

The given parameters are:

Distance = 450 miles

Tank size = 18 gallons

The least miles per gallon this trip is calculated as:

Miles per gallon = Distance/Tank size

This gives

Miles per gallon = 450/18

Evaluate the quotient

Miles per gallon =25

Represent as an inequality

x >= 25

Hence, the least miles per gallon this trip is 25 miles per gallon

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Answer:

229.37, 229.4

Step-by-step explanation:

1. Hundredths
2. Tenths

Answer:

[tex]x > 60[/tex]

Step-by-step explanation:

[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)

Answer: 20 and 14

Step-by-step explanation:

Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.

[tex]20^2 = 400\\14^2=196[/tex]

[tex]20^2-14^2 = 204[/tex]

A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.

Hope this helped :)

Answer:

14 and 20

Step-by-step explanation:

Let x and y be two numbers where x < y.

We are given :

y - x = 6

y² - x² = 204

Then

y - x = 6

(y - x)(y + x) = 204

Then

y - x = 6

6 × (y + x) = 204

then

y - x = 6       (Equation 1)

y + x = 34    (Equation 2)

Then

(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20

Now ,we substitute y by 20 in equation 1 :

y - x = 6

⇔ 20 - x = 6

⇔ 20 - 6 = x

⇔ x = 14

Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

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Answer:

Step-by-step explanation:

1479

Answer:

136

Step-by-step explanation:

While there is no picture for this question, I was able to find this question online, so that should be the correct answer.

19 trees should be planted to maximize the total

From the question, we have the following parameters:

Number of apples, x = 18

Yield, f(x) = 80 per tree

When the number of apple trees is increased (say by x).

We have:

Trees = 18 + x

The yield decreases by four apples per tree.

So, we have

Yield = 80 - 4x

So, the profit function is

P(x) = Apples * Yield

This gives

P(x) = (18 + x) *(80 - 4x)

Expand the bracket

P(x) = 1440 - 72x + 80x - 4x^2

Differentiate the function

P'(x) = 0 - 72 + 80 - 8x

Evaluate the like terms

P'(x) = 8 - 8x

Set P'(x) to 0

8 - 8x = 0

Divide through by 8

1 - x = 0

Solve for x

x = 1

Recall that:

Trees = 18 + x

So, we have

Trees = 18 + 1

Evaluate

Trees = 19

Hence, 19 trees should be planted to maximize the total

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